The proper performance of the first-order reliability method (FORM) is main issue in structural reliability analysis that is dependent on the accuracy, efficiency, and robustness of the employed algorithm. In this paper, a new reliability analysis framework is presented to improve the performance of the first-order reliability method. The innovation of the proposed method, which is a development on the non-negative constraint method, accounts for the estimation of the step size to implement line search formulation. The non-negative constraint method is considered to generate a positive Lagrangian function, an unconstraint optimization problem, and a search direction vector. Then, the first-order Taylor approximation of the positive constraint is applied to find the trail design point. The next step is to consider this trial design point and Pade approximation of the non-negative limit state function (constraint) for appropriately computing the step size. The efficiency and robustness of the proposed algorithm shown in various benchmark numerical examples included a comparison with other first-order reliability methods. The numerical results indicate that the proposed method functions properly to pinpoint the reliability index by fast convergence rates compared to other methods.